Well, when finding the area under a curve all you have to do is find the area under the top curve and then subtract the area from the bottom curve;
so, from -1 to 3 we see that the top curve is the x-axis and the bottom curve is f(x), then from 3 to 4 the top curve if f(x) and the bottom curve is y=0

Well, when finding the area under a curve all you have to do is find the area under the top curve and then subtract the area from the bottom curve;
so, from -1 to 3 we see that the top curve is the x-axis and the bottom curve is f(x), then from 3 to 4 the top curve if f(x) and the bottom curve is y=0

thanks so much, makes sense, as I was trying to work out the height of the triangle, and not getting anywhere.

Also what is the equation of this straight line?

Just to clarify, could we have also worked out where this straight line intersects the curve, therefore the height, and use that to find the area or the triangle and add it to the area of the curve, found by integration?

thanks so much, makes sense, as I was trying to work out the height of the triangle, and not getting anywhere.

Also what is the equation of this straight line?

Just to clarify, could we have also worked out where this straight line intersects the curve, therefore the height, and use that to find the area or the triangle and add it to the area of the curve, found by integration?

Is this a valid method aswell?

The area in the right of the picture is not a triangle, so you can't find the height or anything like that That area is made by a curve and a line.

I think the best way to solve this kind of problems is what sponsoredwalk showed to you